Math 101 (or, mith teaches again)

[mith]

I'm not sure how many people know this already, but I'm teaching this year at my mother's school. I've already started my lesson plans and such, but I decided I wanted to start a thread here for a few reasons:

1. I'm wondering how the classes you took went. I've got my own experiences of course, but it's been a long time since I actually took these classes (it's been... 12 years since I took Geometry). I've also taught some of them (at EEEM's school), but that wasn't the whole year. Anyway, I know that they're done differently by pretty much every teacher, book, etc., so I'd like to know what you remember.

2. Suggestions for things I should do = good. Particularly interesting diversions from lectures and grading systems.

3. I might post notes and such, both so that you can catch mistakes, and so you can learn math if you want.

I'm teaching Geometry, Algebra 2, Pre-cal, and Calculus, btw.

[Bicho the Inhaler]

I took Algebra II and Calculus in high school. Both classes were great.

Algebra II -

- My Algebra II teacher would, for each homework assignment on the day it was due, have each student answer one problem or subproblem. Usually, he would just call on people in turn by going down the rows, but for proofs (e. g., trig identities) we would each get a spot on the whiteboard and we would write out our proofs.

- Homework wasn't graded for correctness, but for completion. There were frequent (graded) quizzes.

Calculus -

- We didn't go over all the problems every class, but every problem that any student had a question about was worked out on the board by another student.

- My teacher was hot.

I think the thing that made both of these classes successful was the way labor was divided during class. Subject-wise, the teacher did only a few things: (1) introduce any new material, going through examples; (2) explain already introduced material (like homework), but only as a back-up. If a homework problem needed to be worked out, it was done by students. Of course, if necessary, the teacher was always able to explain any homework problem.

Your mileage my vary

[Kd]

Well, the UK education system doesn't stretch much further than 'Math' in terms of available mathematics related subjects, but I can still offer some advice if you think it'll help...

My Math teacher wasn't all that great, because he would stand at the board, draw various diagrams, and talk non stop for our entire hour's lesson. Now, diagrams are fine, they help, but droning on for an hour and expecting the whole class to take it all in was just stupid. I'm not expecting you to do that at all, I'm just warning you that it's good to breathe every once in a while.

If you want to create distractions, give your class a GL puzzle! Something along the lines of a code breaker, but with algebra or something. It'll test what your class knows and keep them occupied whilst you make long distance calls from the school telephone. ^_^

I'm never taking Math ever again in my entire life, but I like algebra problems. The way my school's curriculum worked means that I now work better in letters than I do in numbers, so fire away.

Oh, and can you please explain for me why this is a math joke, because I don't get it: 'Let epsilon be less than zero...'

[Dragon Phoenix]

quote:

---

'Let epsilon be less than zero...'

---

LMAO!






















No, I don't get it either....

[Chuck]

Game theory is amusing. You can let them play prisoner's dilemma and ninja combat.

[casinopete]

1. Be "that bastard teacher" everyone has had who requires students to show their work. Especially for calculus or courses that are for advanced students. They need to learn it sometime if they ever intend to go into any scientific field (I would've killed myself over the homework required in my engineering classes if I hadn't been prepped for such exacting requirements in high school).

2. Make plans right now for what to do with that 1, or those 2, or maybe those 5 somewhat slower students who are slowing the class down. If it seems coldhearted to make the plans now, imagine how much worse it will be deciding after you already know the students.

3. Post the first hundred or so digits of pi in large print around the room - it gives the rebelliously bright student something to do while you lecture (he needs something to do since you prohibited playing with a Rubik's Cube for being too distracting).

[Bicho the Inhaler]

Kd, unless I'm missing something, it's a really lame joke. In the branch of mathematics ambiguously and confusingly known as 'analysis,' most proofs begin with the statement "Let epsilon be greater than zero," and those that don't begin with it usually have it somewhere in there. (Roughly, it's because concepts in analysis are often stated in terms of thresholds: "within every threshold, no matter how small, X is true." For historical reasons, 'e,' the lowercase Greek 'epsilon,' is almost always the variable that represents the threshold.) So imagine a mathematician's surprise when he/she sees the statement "Let epsilon be less than zero"...you see? It makes no sense! WAAAAAHAHAHAAA! Unless I'm missing a big part of the picture, there's nothing more to it.

[Bicho the Inhaler]

Originally posted by casinopete:

---

3. Post the first hundred or so digits of pi in large print around the room - it gives the rebelliously bright student something to do while you lecture (he needs something to do since you prohibited playing with a Rubik's Cube for being too distracting).

---

I think "rebelliously bright" students have better things to do than stare at the decimal expansion of pi with a slack-jawed drool. ( )

[casinopete]

Perhaps this theoretical student knew the material, and his teacher was repeating for the benefit of the slower students - which left him decidedly bored. Plus, he was required to remain quietly in his seat for the duration of the class period, but without reading or playing with puzzles or a calculator. What better things could he have been doing?

[casinopete]

Bah. Nevermind. I see the point. The suggestion should be more along the lines of "provide interesting ways for the quicker students to spend their time so they won't waste their time staring, slack-jawed and drooling, at the decimal expansion of pi."

[Kd]

Mmmmm.... pi....

Thanks for explaining that, Bicho. I had no idea how funny (or not) it was meant to be, so I'm glad that's cleared up.

[This message has been edited by Kd (edited 07-16-2003 02:15 PM).]

[Vinny]

Originally posted by Archived Jokes thread:

---

Mathematical Sex

Wherein it is related how that Polygon of Womanly Virtue, your Polly Nomial (our heroine) is accosted by that Notorious Villain Curly Pi, and factored (oh, horror).

Once upon a time ( 1/T ), Pretty Polly Nomial was strolling across a field of vectors when she came to the boundary of a singularly large matrix. Now, Polly was convergent and her mother had made it an absolute condition that she never enter such an array without her brackets on. Polly, however, who had changed her variables that morning and was feeling particularly badly behaved, ignored this condition on the basis that it was insufficient and made her way amongst the complex elements. Rows and columns closed in from all sides. Tangents approached her surface. She became tensor and tensor. Quite suddenly, two branches of a hyperbola touched her at a single point. She oscillated violently, lost all sense of directrix, and went completely divergent. As she reached a turning point, she tripped over a square root that was protruding from the erf and plunged headlong down a steep gradient. When she rounded off once more, she found herself inverted, apparently alone, in a non-Euclidian space.

She was being watched, however. That smooth operator, Curly Pi, was lurking innerproduct. As his eyes devoured her curvilinear coordinates, a singular expression crossed his face. He wondered, Was she still convergent? He decided to integrate improperly at once.

Hearing a common fraction behind her, Polly rotated and saw Curly Pi approaching with his power series extrapolated. She could see at once by his degenerate conic and dissipative terms that he was bent on no good.

"Arcsinh," she gasped.

"Ho, ho," he said. "What a symmetric little asymptote you have. I can see your angles have a lot of secs."

"Oh, sir," she protested, "keep away from me. I haven't got my brackets on."

"Calm yourself, my dear," said our suave operator. "Your fears are purely imaginary."

"I, I," she thought, "perhaps he's not normal but homologous."

"What order are you?" the brute demanded.

"Seventeen," replied Polly.

Curly leered. "I suppose you've never been operated on."

"Of course not," Polly replied quite properly. "I'm absolutely convergent."

"Come, come," said Curly, "let's off to a decimal place I know and I'll take you to the limit."

"Never," gasped Polly.

"Abscissa," he swore, using the vilest oath he knew.

His patience was gone. Coshing her over the coefficient with a log until she was powerless, Curly removed her discontinuities. He stared at her significant places, and began smoothing out her points of inflection. Poor Polly. The algorithmic method was now her only hope. She felt his hand tending to her asymptotic limit. Her convergence would soon be gone forever.

There was no mercy, for Curly was a heavyside operator. Curly's radius squared itself; Polly's loci quivered. He integrated by parts. He integrated by partial fractions. After he cofactored, he performed rungecutta on her. The complex beast even went all the way around and did a contour integration. Curly went on operating until he had satisfied her hypothesis, then he exponentiated and became completely orthogonal.

When Polly got home that night, her mother noticed that she was no longer piecewise continuous but had been truncated in several places. But is was too late to differentiate now. As the months went by, Polly's denominator increased monotonically. Finally, she went to the L'Hopital and generated a small but pathological function that left surds all over the place and drove Polly to deviation.

The moral of our sad story is this: 'If you want to keep your expressions convergent, never allow them a single degree of freedom...'

---

[mith]

Perhaps I should mention that these will be very small classes. My calculus class is probably going to be 2 students.

[Ghost Post]

make them fight for your entertainment. (you can make a little extra cash selling tickets)

[Lucky Wizard]

When I took calculus, at the beginning of each day, my teacher would put a warm-up problem on the board for the students to solve. Usually, this would be a review of the previous day's lesson, but from time to time, we'd get a problem that would be a lead-in to connect the previous day's lesson to that day's upcoming lesson.

On diversions: http://www.math.hmc.edu/funfacts/ might be a good source of diversions. Also, Martin Gardner's Mathematical Games articles can be found in books these days; a list of the books is at the beginning of http://www.ms.uky.edu/~lee/ma502/gardner5/gardner5.html . You might be able to find some good diversions there.

[Bicho the Inhaler]

casinopete, I was totally joking. For the record, I think putting up the digits of pi is a great idea.

[Lucky Wizard]

I'm not sure whether this interests you, but I just remembered this: my calculus teacher, at one point during the year, had each of us do a report and presentation on a famous mathematician or an interesting mathematical topic (such as the Fibonacci series). If this interests you, you could have a class do something like that.

If you want examples, I'll send you the files I made for my report and presentation.

BTW, for the presentation, he let us choose between using Powerpoint and making a posterboard.

[Beartalon]

What I liked most about math were the problems to solve, but the boring word problems! "Jane has 17 eggs, Bob has 12. How many eggs does Sally need to win a fight?" or something asinine like that. There was no application to real life.

I've had a few math teachers who did variations on the word problems that we enjoyed, even if they were sometimes morbid. Word problems about the economics of buying a car, population problems, and financial issues (algebra and calculus), architectural problems (trigonometry and geometry), etc.

One final exam in calculus included a dead body. From the information given about temperature loss we had to determine the approximate time of death. Another problem was what optimal angle to cut a tall man's legs so he'd fit inside a smaller coffin.

[MatthewV]

Use markers that smell good and give you live headed feeling. Your class will be popular, but maybe not with the crowd you like.